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P(n) = the number of integer partitions of n, p(i) = the number of parts of the i-th partition of n, d(i) = the number of different parts of the i-th partition of n, sum_{i=1}^{P(n)} = sum running from i=1 to i=P(n) a(n) = sum_{i=1}^{P(n)} p(i)!/d(i)!

a(4) = 31 because n=4 has the following partitions:

i=1: (1111) with p(1)=4, d(1)=1, 4!/1!=24;

i=2: (112) with p(2)=3, d(2)=2, 3!/2!=3;

i=3: (13) with p(3)=2, d(3)=2, 2!/2!=1;

i=4: (4) with p(4)=1, d(4)=1, 1!/1!=1;

i=5: (22) with p(5)=2, d(5)=1, 2!/1!=2;

Their contributions sum up to 24+3+1+1+2=31=a(4).

A108492 := proc(n::integer) local i, prttnlst, prttn, ZahlTeile, liste, ZahlVerschiedenerTeile, A108492;

# Procedure A108492 calculates the sequence A108492 for the integer partitions of n. prttn = an integer partition of n. See also http://www.thomas-wieder.privat.t-online.de/default.html

prttnlst:=partition(n); A108492 := 0; for i from 1 to nops(prttnlst) do prttn := prttnlst[i]; ZahlTeile := nops(prttn); liste := convert(prttn, multiset); ZahlVerschiedenerTeile := nops(liste); A108492 := A108492 + (ZahlTeile!/ZahlVerschiedenerTeile!); od; print(n, A108492); end proc;

Cf. A007318, A008277.

Sequence in context: A066304 A066165 A119838 this_sequence A003470 A022563 A103939

Adjacent sequences: A108489 A108490 A108491 this_sequence A108493 A108494 A108495

nonn

Thomas Wieder (wieder.thomas(AT)t-online.de), Jun 05 2005